Ditto on sulky....
Sounds like exactly the best thing to do if you want to ruin the patch!
Lilies of the valley is considered a bit of an invasive, in the north, we can't hardly grow it at all down here.
It's been my observation that spreading plants that look good on the edges.... And dead in the middle benefit from being left alone.
At a guess, the spreaders have exhausted the nutrients in the middle... And moving the plants that have escaped into better soil.... Back into the poor soil is not helpful.
Was me....
I'd spread some compost in the middle... And let them recolonized that area in their own time.
